Is there any easy way to check if a piece of music is still under copyright?

I have some obscure rock records from the 60s that I am thinking about converting to digital. How can I check to see if they've gone public so I can add them to the web for posterity without shorting somebody? They weren't very popular back then but a few of us liked them. I'm intrigued by the way the web can be used to preserve things and add to the totality of human culture.